For methods such as BS, WBS and their extensions,
the test statistics associated with change point estimators are
dependent on the previously detected ones, and thus
it is challenging to derive their asymptotic null distributions.
Instead, the thresholds are often given by a range depending on
\(n\) , the level of noise and other typically unknown quantities
such as \(\min _j \vert d_j \vert \)  and \(\min _j \delta _j\) ,
see [1]}, [2]}, [3]}, [4]}, [5]}, [6]}.
[7]} provide a detailed analysis of the tail probability of
\(\max _{(s, k, e) \in \mathcal {I}_3} \vert \mathcal {T}_{s, k, e}(X) \vert \) 
under i.i.d Gaussianity, which enables the selection of the threshold at a prescribed significance level.
